Does accumulating money to build a house count as "circumstances" that justify lowering a due amount, and is the money saved as a result unlawful? And must a mother make up missed prayers after forty days of her postpartum bleeding if she does not remember the blood exiting?

If the bleeding of nifas (postnatal bleeding) stops and the woman in nifas becomes pure, ghusl (ritual bath) and prayer become obligatory upon her. If your mother confirms her purity by one of the two signs of purity (al-qassah al-bayda' - white discharge, or al-jufūf - dryness), then everything that is obligatory upon a non-nifas woman, such as prayer and fasting, becomes obligatory upon her. She should not wait for the completion of the forty days. If she does not pray after her purity, she must make up all the missed prayers. However, if she does not confirm the cessation of bleeding during the forty-day period, she is not obligated to make up prayers for that duration. Regarding the teacher and the price reduction, there is no harm in that, and the amount she waived is permissible (halal).